A candidate scores 25% and fails by 60 marks, while an another candidate who scores 50% marks ,gets 40 marks more than the minimum required marks to pass the examination.Find the maximum marks for the examination.

Answer

To solve the problem, we need to find the maximum marks for the examination based on the information given about two candidates' scores.

### Step-by-Step Solution:

1. **Define Variables**:
Let the maximum marks for the examination be \( X \).

2. **First Candidate's Score**:
The first candidate scores 25% of the maximum marks. Therefore, their score is:
\[ \text{Score of Candidate 1} = 0.25X \]
The candidate fails by 60 marks, which means if they had scored 60 marks more, they would have passed. Thus, the passing marks can be expressed as:
\[ \text{Passing Marks} = 0.25X + 60 \]

3. **Second Candidate's Score**:
The second candidate scores 50% of the maximum marks. Therefore, their score is:
\[ \text{Score of Candidate 2} = 0.50X \]
This candidate scores 40 marks more than the passing marks, so we can express this as:
\[ \text{Score of Candidate 2} = \text{Passing Marks} + 40 \]

4. **Set Up the Equation**:
Since both expressions represent the passing marks, we can set them equal to each other:
\[ 0.50X = (0.25X + 60) + 40 \]

5. **Simplify the Equation**:
Combine like terms on the right side:
\[ 0.50X = 0.25X + 100 \]

6. **Isolate \( X \)**:
Subtract \( 0.25X \) from both sides:
\[ 0.50X - 0.25X = 100 \]
\[ 0.25X = 100 \]

7. **Solve for \( X \)**:
Multiply both sides by 4 to solve for \( X \):
\[ X = 100 \times 4 = 400 \]

8. **Conclusion**:
The maximum marks for the examination is \( 400 \).

### Final Answer:
The maximum marks for the examination is **400**.